I have an eastward facing sliding glass door in my bedroom. During the morning, the beating California sun cooks the room, raising it to 80-90 degrees F (26-32 Celsius) by 9 AM. While the blinds don't block all of the light, they do a good enough job that I'm worried the heat is coming from the large air gap between the glass and blinds (given the size of the door/window), and/or that the flip side of the blinds are being cooked (as evident by them looking burnt), which then emit heat into the room.
I've thought of blackout curtains, but the current blinds are already doing a mostly okay job with the light. The blackout curtains wouldn't eliminate the air gap between the glass and them, and would presumably be cooked by the sun in lieu of the blinds (or not help in that regard if I put them over the blinds rather than replacing them). I could also leave the bedroom door open at night to get better circulation, but then this ends up warming the rest of the house. I'd prefer to keep it out from the beginning.
Are there any in between steps I can take to reduce the heat gain short of replacing the entire glass pane with tinted/multi-pane w/ heat-resistant gas or replacing the whole door?